Kinim, Chapter Two, Mishnah Five
1) Hatat [birds] are on one side, and olot [birds] are on the other and an unassigned [pair] is in the middle:
a) If from the middle pair one bird flew to this side, and one bird flew to this side, then he has not lost anything, because he [the priest] says that the bird that flew [from the middle] towards the hataot is a hatat and the bird that flew towards the olot is a burnt-offering.
b) If one [from each side] returns to the middle, then [all] those in the middle must be left to die, but those [left on either side] can be offered up as hataot or as olot respectively.
c) If again a bird [from the middle] returned and flew away to the sides, then all must be left to die.
2) One cannot pair turtle-doves with pigeons or pigeons with turtle-doves. How is this so?
a) If a woman has brought a turtle-dove as her hatat and a pigeon as her olah, she must then bring another turtle-dove as her burnt-offering;
b) If her olah had been a turtle-dove and her hatat a pigeon, then she must bring another pigeon as her olah.
c) Ben Azzai says: we go after the first [offering].
3) If a woman brought her hatat and then died, her heirs must bring her olah;
a) [But if she first brought] her olah and then died, her heirs need not bring her hatat.
Section one: This section discusses a case where a person has three groups of birds. On one side are a group of birds designated to be hataot. On the other side are a group of birds designated to be olot. In between the two groups is an unassigned pair of birds, one in which it has not yet been determined which will be a hatat and which will be an olah. The mishnah describes three scenarios.
A) If one of the unassigned birds flies to each of the other groups, there is no problem, because these birds can be either a hatat or an olah.
B) If one of the birds from the hataot and one of the birds from the olot flies back to the middle, then they must be left to die because we don’t know which one is a hatat and which is an olah. The birds left on the side remain hataot and olot.
C) If the middle birds now fly back one to each side and become mixed up with the birds there, then the ones on the side must die as well because we don’t know which are hataot and which are olot.
Section two: When a woman brings a pair of birds for sacrifices she must either bring two turtle-doves (and a partridge in a pear tree) or two pigeons. She cannot bring one of each type of bird.
According to the first opinion, the hatat is the bird that determines what the other bird must be. So if the hatat is a turtle-dove, she must bring a turtle-dove as an olah, and if the hatat is a pigeon, she must bring a pigeon as an olah. The order in which the birds are brought does not matter.
Ben Azzai says that the first bird that she brings determines what the second bird is. Therefore if she first brings a turtle-dove as an olah, and then tries to bring a pigeon as a hatat, she must bring a turtle-dove as an olah.
Section three: If a woman sets aside birds as sacrifices and then dies, her heirs can offer the olah but they cannot offer the hatat, because a hatat whose owners have died must be left to die. This is the standard rule with regard to the hatat (see Temurah 2:2).